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The characterization of best nonlinear Tchebycheff approximations

Citation

Rice, John Rischard (1959) The characterization of best nonlinear Tchebycheff approximations. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd-02102006-083607

Abstract

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Consider a continuous function, F([...]) of n parameters and [...]. Such a function is said to have Property NS if the following theorem is valid for every continuous function, f(x):

THEOREM: F([...]) is a best approximation to f(x) if and only if there are n+1 distinct points, [...], such that [...].

Depending an the basic assumptions on F, several sets of necessary and sufficient conditions are given for F to have Property NS. These conditions involve unisolvence and related concepts. The definition of Property NS is generalized and necessary and sufficient conditions on F are given for F to have this generalized property. The latter theory includes most common nonlinear approximating functions.

Item Type:Thesis (Dissertation (Ph.D.))
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Mathematics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Erdelyi, Arthur
Thesis Committee:
  • Unknown, Unknown
Defense Date:1 January 1959
Record Number:CaltechETD:etd-02102006-083607
Persistent URL:http://resolver.caltech.edu/CaltechETD:etd-02102006-083607
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:594
Collection:CaltechTHESIS
Deposited By: Imported from ETD-db
Deposited On:10 Feb 2006
Last Modified:26 Dec 2012 02:30

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